FinalSolution - AAE 333 Final Exam Open Book 1 Crib sheet...

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AAE 333 Final Exam Dec 16 2009 Open Book, 1 Crib sheet allowed The right answer is worth 5 points. A wrong answer is worth 0. Fill in the circle on the scantron sheet corresponding to your answer chosen from the list provided. Hand in the scantron sheet separately. NOTE: I will post a detailed solution later, for anyone interested (possibly on Sunday) 1. A 2D velocity field u=A1 *y, v=A2*x exists with constants A1 and A2. (Units are MKS). Determine the values of A1 and A2 required for the flow to be irrotational and the volume flow rate passing up through the line segment from (x,y)=(0,0) to (1,0) to be 2 m^3/s/m a. A1=4 ; A2=4 b. A1=4; A2=-4 c. A1=2; A2=-2 d. A1=2; A2=2 e. A1=1; A2=4 f. A1=4; A2 = 1 IRROTATIONAL -> 0 = vorticity = curl(vel) = dudy-dvdx = A1-A2 VFR = int (v dx) from x=0 to 1 on y=0 = int(A2 x dx) = A2 (x^2/2 at 1 – x^2/2 at 0) = A2/2 = 2
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So A1=A2 = 4 2. The density of liquid water is closest to This is how the unit of mass was defined in SI units… 1gram= mass of 1cc of water 1 m^3 is 1e6 cc has mass of 1e6 g or 1e3 kg 3. A spherical balloon has a volume of 1000 m^3. The density of the gas inside is 0.1 kg/m^3. The density of the gas outside is 1kg/m^3. The acceleration of gravity is 10 m/s^2. What is the net upward force on the balloon? F= Fbouyant – Fweight = weight of displaced air – wejght of gas inside = g Vol (rho_air – rho_gas) = 10*1000**(1-.1) = 9000
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4. A flat plate extends from (x,y)=(0,0) to (3 ,0). The gage pressure on the bottom surface is -100x. The gage pressure on the top surface is 0. The moment about the (0,0) end (positive clockwise) is NOTE: Because the unintentional mark at the end of line 1 could be interpreted as a minus sign, I regraded to allow full points for either c. or d. If the gage pressure is +100x the answer is d. If it’s -100x the answer is c. I had intended +100x and do not know where the dash came from. dFy = deltap dx = y force on element dx at x dMz = -x dFy = clockwise moment of elemental force about x=0 Mz = int(dMz) from x=0 to 3 Take delatap=100x (ie ignore dash in line 1): Mz = -100 int(x^2 dx) = -100 (x^3/3 at 3 – x^3/3 at 0) = -100 3^3/3 = -900
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